My advice before you go buying items you'll only use once or twice. Use a hair dryer on high first. Plastic razor blades are always a good buy and they are cheap. (Always good to have them around the house anyways).
Depending on your skill level I would hate for you to do one (or both) of two things: melt the plastic your handles are made of OR damage the paint with too much heat. I'm not saying you will but its always better to be on the safe side then shoot your own foot.
APC or even Acetone (with a tooth brush or a brush with soft bristles) after you work your magic with heat and plastic razor (maybe we do not mix with the heat bc it is pretty flammable, please don't go dying on us) and followed with the products like the one mentioned above aerospace 303 (I think someone did a write up of that not too long ago). Or if you want to get everything from Walmart or auto store instead of waiting on the postman to deliver your goods, you could try a cheapo product like Turtle Wax trim restorer or similar type of product if you're on somewhat of a budget or just want it to look decent without a ridiculous amount of work.
Trim restore compound on Amazon.
This two should do the trick. No need to go to paint shop. 1-2 hrs of scrubbing and it should be just like new.
Ohhhhh.
I use Turtle Wax Trim Restore on my dip to protect it, hasn't caused any problems in a few years.
Amazon links put you in the spam queue. Especially when they've got affiliate codes in them (the tag=
part).
You need to clean that link up before I can approve it. Something like this is allowable.